Study On Fractal Interpolation Curves Based On Dimensions In Virtual Environment

The fractal theory is a very active branch of modem mathematics and non-linear theory. In the last decade, it has played an increasingly important role in image processing and analysis. Many reports have been made about the applications of fractal theory in the fields of natural image simulation, image texture analysis, pattern recognition etc. Combined with the question that how to simulate a better fractal image in Computer VR(virtual reality) environment, this paper has made some remarkable and fruitful results by going deep into the detailed study about the fractal mathematical theory, especially the fractal dimension theory and fractal dimension computing. The key work involves:a. Based on the current research work, a method has been provided that the fractal dimension of the FIF (fractal interpolation function) image should be the same with that of the original image in the Computer VR environment, and then the fractal image is more similar to the original image.b. Some remarkable and fruitful results have been made by going deep into the detailed study about the fractal mathematical theory, especially the fractal dimension theory and fractal dimension computing. Using the popular method to compute Box dimension. Some error also has been given.c. Base on the research of the fractal interpolation method, the method of linear fractal interpolation function has been discussed in detail.